We critically reexamine two possible Dark Matter candidate within the Standard Model. First, we consider the $uuddss$ exa-quark. Its QCD binding energy could be large enough to make it (quasi) stable. We show that the cosmological Dark Matter abundance is reproduced thermally if its mass is 1.2 GeV. However, we also find that such mass is excluded by the stability of Oxygen nuclei. Second, we consider the possibility that the instability in the Higgs potential leads to the formation of primordial black holes while avoiding vacuum decay during inflation. We show that the non-minimal Higgs coupling to gravity must be as small as allowed by quantum corrections, $|ξ_H| < 0.01$. Even so, one must assume that the Universe survived in $e^{120}$ independent regions to fluctuations that lead to vacuum decay with probability 1/2 each.

31 pages, 11 figures. v2: final version to appear on PRD; added comments about arXiv:1805.03723